Questions tagged [self-study]

This tag means the asker is new to the DSP field and is requesting extra guidance. It has similar connotations to the homework tag, but this lets potential answerers know they should probably do more than guide the self-studier compared with the homework requester.

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66 views

Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
1 vote
2 answers
146 views

How can I apply a filter to remove reverberation with python?

I am developing an algorithm that automates the processing of audio files for the assembly of datasets of machine learning models. Among the steps to be followed for the processing of the files is to ...
1 vote
0 answers
21 views

implement gradient descent with sparsification algorithm

I am trying to implement the algorithm in this paper for finding a sparse vector x that minimizes the square error $\lVert y − \Phi x\rVert_2^2$ where $\Phi$ need to satisfy the restricted isometry ...
0 votes
2 answers
174 views

Calculating connected component's central moments

I am learning about image's moments. As an exercise I got this: For x̄ value I get 5 from this formula: $$= \frac{\sum_{x=1}^{X} \sum_{y=1}^{Y} xf(x,y)}{\sum_{x=1}^{X} \sum_{y=1}^{Y} f(x,y)}$$ As ...
1 vote
1 answer
227 views

The Math of Histogram Matching

Please help solve the problem in the picture. I am confused due to the piecewise nature of the density functions. If it was a simple curved PDF, I would simply integrate over full range and use the ...
1 vote
1 answer
71 views

How to learn image processing in an applicational way?

My question is for image processing and computer vision "practitioner" who study on a company. Since I have an degree on electrical engineering and mathematics, I have signal processing, ...
3 votes
2 answers
55 views

Confusion regarding lacunarity of koch curves with same fractal dimension but different orders

I'm trying to use the concept of lacunarity to classify images, as per how a few research papers have done it. To verify whether my equations and implementation are correct, I'm trying to verify the ...
0 votes
1 answer
162 views

Should we use all $N$ correspondence points to compute Homography or just $4$ points?

Given correspondences of $(x,x')$, we want to find a Homography matrix $H$ that maps $x' = Hx$. If we use 4 corresponding non - collinear points and the matrix $H$ has rank $n-1$, then the homogenous ...
0 votes
1 answer
56 views

Magnitude spectrum of LTI system output signal

First year student so please excuse my lack of knowledge. As i understand i need to use convolution which is: $$ y^{out}(t) = u^{in}(t) * h(t) $$ Or maybe my thoughts are wrong so please correct me. ...
1 vote
1 answer
54 views

Plotting the amplitude and angle spectre of this signal

I am looking clarification that I have the appropriate solution to this question, thoughts and tips to improve my understanding are also welcome! f(n) is a discrete sample of the following signal. ...
0 votes
1 answer
61 views

Determining the full DFT values of X(k) given a partial sample [closed]

I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial. I am thinking that I am going to work back, I read the matlab documentation ...
-1 votes
1 answer
81 views

Expected value and autocorrelation

I have a wide sense stationary stochastic process ${{X_t;t\in \Re}}$ with mean 0 and autocorrelation function $R_x(\tau)=1-\frac{1}{4}|\tau|$ for $|\tau|=0,1,2,3;$ and zero anywhere else. I'm supposed ...
2 votes
1 answer
116 views

Expressing the frequency response in a more 'compact' form

I've just been working through the questions in Discrete-Time Signal Processing (Oppenheim and Schafer) and I came across this (Q33): Consider an LTI system defined by the difference equation $$y[n] =...
0 votes
1 answer
312 views

Constant modulus algorithm - performance poor?

The question is based on a research article titled, "Novel Robust Blind Equalizer for QAM Signals Using Iterative Weighted-Least-Mean-Square Algorithm" The Authors have proposed an equalization ...
6 votes
2 answers
1k views

Why are equalizers moving average model (FIR)

Let the equalizer coefficients obtained, say $w$ and the input to the equalizer is $y$ that is a noise corrupted received signal, $rx$ then the equalized signal, which is the output of the FIR based ...
0 votes
1 answer
371 views

Simulate butterworth filter with initial condition of state vector in R

I'm working in R with the packages signal and control (don't know wether these are even the best for my use case). I have a high ...
-1 votes
1 answer
461 views

How can I find expansion coefficients of the a vector in a given basis?

How can I find the coefficient of the vector $\mathbf y$? And how can the inner product be done on these vectors? Let $\mathbf y = \begin{bmatrix}1\\2\\0\\1\end{bmatrix}$ What are the expansion ...
54 votes
16 answers
40k views

What Resources Are Recommended for an Introduction to Signal Processing (DSP)?

What are some recommended resources (books, tutorials, lectures, etc.) on digital signal processing, and how to begin working with it on a technical level?
1 vote
1 answer
159 views

What is a correct approach to baud-rate digital timing recovery for self-equalized line code

In particular, I have a signal coming from a twisted pair of arbitrary length with a differential encoded biphase line code. What should be a correct approach to timing recovery in this case? ...
5 votes
1 answer
682 views

LMS Convergence and the Step Size ($ \mu $) Parameter

I am running the LMS algorithm based on Haykin's Adaptive filter theory. I aim to plot the cost function $\mathbf{J}$ and calculate $\mathbf{J}_{\tt min}$ and the simulation excess mean square error $\...
7 votes
2 answers
909 views

Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below: I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading ...
0 votes
3 answers
17k views

Matlab: Correct method of generating Rayleigh fading channel

A Rayleigh flat fading channel has 1 tap and so there will be no intersymbol interference. if N= 1000; Then, h=(1/sqrt(2))*(randn(N,1)+1i*randn(N,1)); will ...
0 votes
1 answer
85 views

Probability of achievable data rate greater than target data rate $\Pr\left[\frac{1}{2}\log_2\left(1+\text{SINR}\right)>R_{\text{target}}\right]$?

I came across this formulation of the probability that the achievable data rate is greater than the target data rate for the NOMA system. $$\Pr\left[\frac{1}{2}\log_2\left(1+\text{SINR}\right)>R_{\...
0 votes
1 answer
38 views

What does $\mathcal{ E}(|h|^2)$, where $|h|^2$ is power of the channel gain $h$ represent?

I came across this notation of $\mathcal{E}(|h|^2)$ in a research article. $h$ is the channel gain of a wireless communication channel. In particular, a Rayleigh fading channel. I know that $|h|^2$ ...
1 vote
1 answer
168 views

How to choose a fixed adaptation step for decision feedback equalizer

How do I choose $\mu$ - a value of a step size for adaptation in a decision feedback equalizer (DFE) with adaptive reference control (ARC)? For a regular adaptive FIR filter an adaptation step depends ...
0 votes
1 answer
33 views

Running a signal through a circuit with some odd components

I am studying a course in signal analysis and systems. Currently we are looking at aliiasing, samplig,DTFT and reconstruction. I got stuck on an excercise. For the in signal $x_{a}(t)=2\cos(2\pi F_{0}...
1 vote
1 answer
75 views

FInd the amplitude function to a system

I'm studying a course in signal analysis and have come across an exercise where I find the analytical part a bit tricky. I am to find the amplitude function $|H( f )|$ for a system with the impulse ...
0 votes
1 answer
471 views

Filtering White Noise to Generate Harmonic Signal

I have studied convolutions and filters a long time ago. Today, I am trying to review the basics using some notes of mine, but I am finding difficult to solve easy problems. Since I don't have ...
0 votes
1 answer
33 views

Zeroes and poles for a system

I have run into some issues on an exercise for the course in signal analysis and systems I am currently studying. We are to create an echo effect and are using the system below: I am to find the ...
1 vote
1 answer
262 views

What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc...)? [closed]

I would like to improve my knowledge about Fourier Transform and related subjects. What are the recommended resources in order to self study about it?
6 votes
2 answers
18k views

Interview Questions for a DSP Engineer

I am preparing an interview which may require some knowledges on DSP. Is there any questions, fundamental concepts, and theories that I would not want miss? Thanks a lot for the suggestions.
7 votes
3 answers
8k views

What are your tips for DSP self-study?

Perhaps a meta-question, but I'll post it here because some of you are bound to possess gold nuggets about continuing education. It might be closed for being subjective but I don't care because this ...
1 vote
1 answer
340 views

Unit step function symbol

I've been studying communications and i see that the book used the symbol $u_{-1}(t)$ for unit step function , why ?
2 votes
2 answers
643 views

Recommendation for courses / studies on digital signal processing

I hold a master's degree in mechanical engineering. However at my job I am more and more diving into topics of signal processing and data science. I find it great to discover about new topics and to ...
2 votes
2 answers
605 views

Inverse system of sinc?

I'm doing some self-study for an important exam I'll have in late March and came across the following question: So, using the convolution properties, if I want to find an identity system so that the ...
1 vote
1 answer
899 views

Finding optimal decision threshold for binary comm system

I'm trying to solve the following exercise: Given a system that transmits bit $b$ with probability $p_b$ and $-b$ with $p_{-b}$ and the transmission is degraded by AWGN $N(0,\sigma^2)$. What is the ...
1 vote
1 answer
370 views

Effect of sampling rate on BER simulation

I am trying to build a bit error rate simulation for a digital baseband signal (specifically using Manchester coding). The simulator generates a digital waveform from random symbols at a sample rate ...
0 votes
1 answer
90 views

Inverting a sampled system

I'm doing some self-study for an upcoming exam and came across the following question: My first idea to solve it was using the bilinear transform to get some approximation of $H(Z)$ (or just using ...
3 votes
1 answer
9k views

Matlab: What is the proper way to calculate mean square error for complex numbers

I am confused regarding the calculation of mean square error involving complex numbers. Considering, the true channel coefficients to be ...
0 votes
1 answer
125 views

Finding the discrete time fourier coefficients to this problem

I'm trying to find the fourier series to this discrete time signal. $$x_1[n] =\begin{cases} +\frac72&\text{if }0\le n \le 4\\ -\frac72&\text{if }5\le n \le 9 \end{cases}$$ My approach: We see ...
1 vote
1 answer
139 views

Evaluate expressions without computing DTFT

Let $X(\omega)$ be the DTFT of the sequence $x[n]$ given by: $$ x[n] = \{4, 2, -1, 5, -3, 1, -2, 4, 2\},\quad\text{for}\quad n \in [-6, 2] $$ I do want to compute $X(0)$ $X(\pi)$ $\displaystyle\int_{-...
2 votes
2 answers
3k views

Find power of a sum of sinusoids

We got this question to solve: Calculate the power of the signal: $$s(t) = 8\cos\left(20\pi t-\frac \pi4\right) + 4\sin(15\pi t)$$ Now, I thought of two approaches : Use Parseval theorem, so first ...
0 votes
0 answers
25 views

Best way to compare audible alarms

I'm working on an alarm recognition program in MATLAB in which multiple reference audio samples of different alarms would be recorded. Afterwards, the program would sample every so often and compare ...
0 votes
2 answers
90 views

Convert complex valued sinusoid to real valued sinusoid

This is the homework problem: convert $x[n]=je^{j\pi n/8}-je^{-j\pi n/8}$ to a real valued sinusoid. I understand that $\sin\theta=\dfrac{e^{j\theta}-e^{-j\theta}}{2j}$ In the solution, the answers ...
0 votes
1 answer
278 views

Coefficients of a Zero Forcing linear equalizer for infinite length input

Given a discrete-time white noise model: $$y_k = \sum_{i=0}^{\infty} \alpha^{-i}a_{k-i} + \eta_k$$ where $E(|a_k|^2)=2$, $|\alpha|>1$, $\eta_k$ are uncorrelated zero mean random variables with $E(|\...
0 votes
0 answers
213 views

Degradation of BPSK system using matched filter with a timing error

Given a BPSK system with: \begin{align*} s_1(t) &= Au_T(t) \\ s_2(t) &= -Au_T(t) \\ \end{align*} where $u_T(t)=1$ for $0<t<T$, and zero otherwise. Given $A > 0$, and Gaussian white ...
1 vote
1 answer
962 views

Block diagram of filter

Can you help me with this question. Can you explain where i should start to solve the problem.
2 votes
2 answers
64 views

Clarification on eigenfunction property from Oppenheim's Discrete-time signal processing, 3rd ed

Could anybody explain what is meant by the following statement on page 50 of Oppenheim and Schafer's book Discrete-Time Signal Processing (third edition)? The eigenfunction property of complex ...
1 vote
3 answers
2k views

How do the magnitude and phase spectrum of an imaginary function look like?

Say I have the function $$x(t)=j \operatorname{rect}(t)$$ Is the phase spectrum even or odd? I am confused whether the phase spectrum is an odd/even function of $\omega$ (angular frequency, Fourier ...
2 votes
2 answers
531 views

Power of an angle-modulated wave

Let $$\phi(t) = A\cos(\omega_c t + km(t)) \tag{1}$$ be an angle-modulated wave(FM or PM). What's the power of $\phi(t)$? Intuitively, it seems that the answer is $$P = \frac{A^2}{2} \tag{2}$$ since ...